1. Field of the Invention
The present invention is directed to an optical element, the method of making the optical element, an optical system using the optical element for an optical apparatus (e.g., a camera, microscope, telescope or photolithographic apparatus such as a stepper, etc.), and a method for calculating the birefringence of the optical element.
2. Description of the Related Art
Calcium fluoride, strontium fluoride and barium fluoride, which are fluoride crystals (single crystals) used as optical element materials, have a low refractive index compared to ordinary optical glass, and also show little dispersion (wavelength dependence of the refractive index); accordingly, such materials are useful for color aberration correction in optical systems.
In particular, calcium fluoride is easy to obtain, and can be obtained even as large-caliber single crystals with a diameter of "PHgr" 150 mm or greater.
Such fluoride crystals (single crystals) belong to the cubic crystal type, and are optically isotropic bodies. These materials are suitable as materials for optical elements such as lenses, etc. Fluoride crystals have long been widely used as materials of camera lenses, microscope lenses and telescope lenses, etc.
Birefringence is a phenomenon in which the refractive index varies according to the direction of polarization of the light or other electromagnetic waves. Ordinarily, this is expressed as the light path difference (called xe2x80x9cretardationxe2x80x9d) that occurs when the light passes through a unit length of the substance in question, and is given in units of nm/cm.
Furthermore, as another method of expressing birefringence, this phenomenon is also sometimes expressed as the difference (n1xe2x88x92n2) between the refractive index n1 with respect to light having a certain direction of polarization and the refractive index n2 for light with a direction of polarization that is perpendicular to the above-mentioned direction of polarization.
Furthermore, the refractive index n0 in a state in which no external force is acting on the substance in question is affected by external forces so that the refractive index changes. In cases where this change is dependent on the direction of polarization, the amounts of change in the refractive index are expressed as xcex94n1 and xcex94n2, and the difference between these amounts of change, i.e., (xcex94n1xe2x88x92xcex94n2), is also sometimes called xe2x80x9cbirefringencexe2x80x9d.
In cases where birefringence is caused by strain, this birefringence is also commonly called xe2x80x9cstrainxe2x80x9d. Moreover, crystals with cubic crystal systems inherently lack birefringence, but may have birefringence as a result of the effects of electromagnetic fields and stress.
Specifically, in the case of the above-mentioned fluoride crystals (single crystals), birefringence is generated as a result of the effects of stress. For example, considerable birefringence is present in currently manufactured fluoride crystals as a result of thermal stress occurring in the manufacturing process. Furthermore, the value of this birefringence is at least about 5 nm/cm, and may commonly reach 10 nm/cm or greater in fluoride crystals with a diameter of "PHgr" 100 mm or greater.
Accordingly, even if an attempt is made to minimize the aberration of an optical system using a fluoride crystal (single crystal), the birefringence of the fluoride crystal arising from the effects of stress is an impediment. As a result, satisfactory optical performance often cannot be obtained in the optical system.
Furthermore, if countermeasures such as an extreme lengthening of the annealing time in the fluoride crystal manufacturing process, etc., are adopted in order to reduce the birefringence of fluoride crystals (single crystals) used in optical elements or optical systems, delivery dates are delayed (i.e., the productivity drops), and costs are increased.
In recent years, there has been a rapid development of lithographic techniques for inscribing integrated circuit patterns on wafers. Demand for higher integration of integrated circuits continues to grow. In order to realize such higher integration, it is necessary to increase the resolving power of stepper projection lenses.
The resolving power of a projection lens is governed by the wavelength of the light used and the NA (numerical aperture) of the projection lens. The resolving power can be increased by shortening the wavelength of the light used or increasing the NA (increasing the caliber) of the projection lens.
First, shortening of the wavelength of the light used will be discussed. The wavelengths used in steppers have already advanced to the g line (wavelength: 436 nm) and i line (wavelength: 365 nm). In the future, when even shorter-wavelength KrF excimer laser light (wavelength: 248 nm) and ArF excimer laser light (wavelength: 193 nm), etc., come into use, the use of optical glass in optical systems will become virtually impossible from the standpoint of transmittance.
Accordingly, synthetic silica glass or calcium fluoride is commonly used as an optical element material in the optical systems of excimer laser steppers.
Next, increasing the caliber of such elements will be discussed. Here, it is not simply a question of better results with a larger caliber. In regard to the materials of optical elements used in the optical systems of excimer laser steppers, it is necessary that single crystals be used in the case of calcium fluoride.
Furthermore, as the performance of steppers has improved, there has recently been a demand for large-caliber calcium fluoride single crystals with a caliber of around "PHgr" 120 mm to "PHgr" 250 mm. Such calcium fluoride single crystals have a low refractive index compared to ordinary optical glass, and also show little dispersion (wavelength dependence of the refractive index). Accordingly, such materials are extremely effective in the correction of color aberration. Furthermore, such materials can easily be obtained in the marketplace, with large-caliber single crystals having a diameter of "PHgr" 120 mm or greater also being obtainable.
Calcium fluoride single crystals which have such advantages have long been used as lens materials in cameras, microscopes and telescopes in addition to being used as optical materials in steppers.
Furthermore, single crystals of barium fluoride and strontium fluoride, which are fluoride single crystals other than calcium fluoride single crystals, belong to the same cubic crystal type, and have similar properties; accordingly, the uses of these crystals are also similar to those of calcium fluoride single crystals.
Such fluoride single crystals can be manufactured by a method known as the Bridgeman method, the Stockberger method, or the xe2x80x9cpull-downxe2x80x9d method.
Here, a method for manufacturing calcium fluoride single crystals by the Bridgeman method (one example) will be described.
In the case of calcium fluoride single crystals used in the ultraviolet or vacuum ultraviolet region, natural fluorite is not used as a raw material; instead, the general practice is to use high-purity raw materials manufactured by chemical synthesis.
The raw materials can be used xe2x80x9cas isxe2x80x9d in a powdered state. In such a case, however, the volume decrease upon melting is severe. Ordinarily, therefore, semi-molten raw materials or pulverized products of the same are used.
First, a crucible filled with the above-mentioned raw material is placed in a growth apparatus, and the interior of the growth apparatus is maintained at a vacuum of 10xe2x88x923 to 10xe2x88x924 Pa.
Next, the temperature inside the growth apparatus is elevated to a temperature above the melting point of calcium fluoride (1370xc2x0 C. to 1450xc2x0 C.) so that the raw material is melted. In this case, control by means of a constant power output or high-precision PID control is performed in order to suppress fluctuations in the temperature inside the growth apparatus over time.
In the crystal growth stage, the crucible is lowered at a speed of approximately 0.1 to 5 mm/h, so that crystallization is gradually caused to occur from the lower part of the crucible.
When crystallization has occurred up to the upper portion of the melt, crystal growth is completed, and a simple gradual cooling process is performed, with sudden cooling being avoided so that the grown crystal (ingot) does not crack. When the temperature inside the growth apparatus has dropped to room temperature, the apparatus is opened to the atmosphere, and the ingot is removed.
Ordinarily, a graphite crucible is used in this crystal growth, and a pencil-shaped ingot with a conical tip is manufactured. In this case, a single crystal can be formed by growing the crystal from the area of the tip end of the conical part positioned at the lower end of the crucible.
Furthermore, if necessary, there is also a technique in which the direction of crystal growth is controlled by placing a seed crystal in the above-mentioned tip end portion; however, if the diameter of the ingot exceeds "PHgr" 120 mm, control of the orientation of crystal growth becomes extremely difficult.
Generally, in cases where a fluoride single crystal is manufactured by the Bridgeman method, it is considered that there is no preference in the direction of growth, so that the horizontal plane of the ingot is a random plane in each crystal growth process.
Since there are extremely large amounts of residual stress and strain in the ingot removed from the crucible, the ingot is subjected to a simple heat treatment xe2x80x9cas isxe2x80x9d.
The fluorite single crystal ingot thus obtained is cut to an appropriate size according to the desired product. Here, the ingot is naturally cut horizontally (annular cut) in order to cut out a material for manufacturing a larger optical element (lens, etc.) from the ingot in accordance with the desired product. Then, the material thus cut out is subjected to a heat treatment in order to improve the quality of the material.
In view of the above circumstances, an object of the present invention is to provide a method for calculating the birefringence of an optical element and a method for determining the birefringence of an optical element that make it possible to select the direction of minimum birefringence in the optical element. A further object is to provide an optical element that has little birefringence. Yet another object of the invention is to provide a method of manufacturing the material used to make an optical element with reduced birefringence. Another object is to provide an optical system in which the aberration of the optical devices is small.
To achieve the objects and in accordance with the purpose of the invention, as embodied and broadly described herein, the invention includes the method of manufacturing an optical element, calculating the birefringence of the optical element and determining the direction of minimum birefringence of the optical element. The method includes cutting a material for manufacturing optical elements from a fluoride single crystal ingot obtained by crystal growth so that the {111} crystal planes are two parallel planes, after which the optical performance is improved by subjecting this material to a heat treatment.
The material for manufacturing optical elements can also be cut from a fluoride single crystal ingot which has been obtained by crystal growth and which has been subjected to a heat treatment, so that the {111} crystal planes are two parallel planes, after which the optical performance is improved by subjecting this material to a heat treatment.
The birefringence of the above-mentioned material for manufacturing optical elements is reduced from a value of 5 nm/cm or greater to a value of 3 nm/cm or less by means of the above-mentioned heat treatment.
The shape of the material for manufacturing optical elements cut from the above-mentioned ingot is a cylindrical shape with a diameter of "PHgr" 120 mm or greater.
Preferably, the above-mentioned fluoride single crystal is a calcium fluoride or barium fluoride single crystal.
Furthermore, since single crystals of calcium fluoride and barium fluoride both cleave along the {111} crystal planes, splitting (cleavage) will occur along the {111} planes in cases where the ingot splits as a result of thermal strain, etc.
Moreover, even in the case of an ingot which shows no cleavage, cleavage will occur if the end portion is struck lightly with a chisel, etc.
If the ingot is cut using the cleaved planes (cleavage planes) as a reference, so that the surfaces of the ingot are parallel to these planes, a material for manufacturing optical elements can be obtained. In the material thus obtained, {111} crystal planes are two parallel planes.
In cases where an optical element (e.g., a stepper projection lens) is manufactured from a material for manufacturing optical elements consisting of a fluoride single crystal of the present invention which has {111} crystal planes as two parallel planes, and which has a birefringence of 3 nm/cm or less, and an attempt is made to minimize the aberration of an optical system using this optical element, the birefringence of the material does not present problems as in conventional methods. As a result, the number of optical elements that can be used in the above-mentioned optical system (i.e., the number of optical elements that can be manufactured from the material) can be increased.
The method of calculating the birefringence of the optical element in accordance with another aspect of the invention includes converting known piezo-optical or elasto-optical constants in a specified three-dimensional orthogonal coordinate system for an optical material into piezo-optical or elasto-optical constants in an arbitrary three-dimensional orthogonal coordinate system. The method further includes calculating the amount of change in the refractive index xcex94n1 of the optical material in a first direction along the direction of one coordinate axis of the above-mentioned arbitrary three-dimensional orthogonal coordinate system, and the amount of change in the refractive index xcex94n2 of the optical material in a second direction which is perpendicular to the first direction. The calculation uses a uniaxial stress or the strain corresponding to the uniaxial stress that is applied to the above-mentioned optical element or optical element material along the first direction, and the piezo-optical or elasto-optical constants in the arbitrary three-dimensional coordinate system. The method also includes determining the difference between the amount of change in the refractive index Anl and the amount of change in the refractive index xcex94n2 to determine the amount of birefringence as seen from a third direction perpendicular to the first direction and the second direction.
Since birefringence arising from stress is closely associated with the amount of displacement (strain), the present invention contemplates that birefringence is also dependent on direction. This fact was confirmed by a careful calculation of physical tensors.
The direction of observation showing a minimum birefringence is found for the above-mentioned optical element or optical element material from the amounts of birefringence respectively determined in the above-mentioned arbitrary three-dimensional orthogonal coordinate system.
According to another aspect of the invention the optical element material can be worked so that the above-mentioned direction of observation showing a minimum birefringence is caused to substantially coincide with the direction of the optical axis.
The material of the optical element can be a fluoride crystal. The fluoride crystal can be selected from a group of materials including calcium fluoride, strontium fluoride or barium fluoride.
The direction of observation showing a minimum birefringence substantially coincides with the  less than 111 greater than  axial direction of the fluoride crystal, or substantially coincides with a direction perpendicular to the {111} plane of the fluoride crystal.
The optical element can be constructed from a fluoride crystal with the direction of the optical axis substantially coinciding with the  less than 111 greater than  axial direction of the fluoride crystal, or substantially coinciding with a direction perpendicular to the {111} plane of the fluoride crystal.
In accordance with another aspect of the invention, an optical system for an optical apparatus can be constructed by combining fluoride crystals with the same refractive index or different refractive indices, and in which the direction of the optical axis of the optical system either coincides or substantially coincides with the  less than 111 greater than  axial direction of at least one of the fluoride crystals, or coincides or substantially coincides with a direction perpendicular to the {111} plane of the at least one fluoride crystal. Reference to a direction that coincides or substantially coincides can preferably encompass coincidence within approximately 5 degrees in angular deviation.
The direction of minimum birefringence in an optical element or optical element material can be selected, so that an optical system with little (minimal) aberration can be constructed by means of such optical elements, or so that an optical element with a small birefringence (in which the direction of the optical axis is set so that the birefringence is minimal) can be obtained from such an optical element material.